Effective non-linear dynamics of binary condensates and open problems

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We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics: for such models, the effective dynamics is described by a coupled system of nonlinear Schödinger equations. After reviewing and commenting our proof in the mean field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

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